A Sample/Population Size Activity: Is It the Sample Size of the Sample as a Fraction of the Population that Matters?

Smith, Margaret H.

Journal of Statistics Education, v12 n2 Jul 2004

Unless the sample encompasses a substantial portion of the population, the standard error of an estimator depends on the size of the sample, but not the size of the population. This is a crucial statistical insight that students find very counterintuitive. After trying several ways of convincing students of the validity of this principle, I have finally found a simple memorable activity that convinces students beyond a reasonable doubt. As a bonus, the data generated by this activity can be used to illustrate the central limit theorem, confidence intervals, and hypothesis testing. (Contains 2 tables.)